Solve for c 2c^2+54=0

$2 c^{2} + 54 = 0$

Subtract $54$ from both sides of the equation.

$2 c^{2} = - 54$

Divide each term by $2$ and simplify.

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Divide each term in $2 c^{2} = - 54$ by $2$ .

$\frac{2 c^{2}}{2} = \frac{- 54}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 c^{2}}{2} = \frac{- 54}{2}$

Divide $c^{2}$ by $1$ .

$c^{2} = \frac{- 54}{2}$

Divide $- 54$ by $2$ .

$c^{2} = - 27$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$c = \pm \sqrt{- 27}$

The complete solution is the result of both the positive and negative portions of the solution.

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Simplify the right side of the equation.

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Rewrite $- 27$ as $- 1 (27)$ .

$c = \pm \sqrt{- 1 \cdot 27}$

Rewrite $\sqrt{- 1 (27)}$ as $\sqrt{- 1} \cdot \sqrt{27}$ .

$c = \pm \sqrt{- 1} \cdot \sqrt{27}$

Rewrite $\sqrt{- 1}$ as $i$ .

$c = \pm i \cdot \sqrt{27}$

Rewrite $27$ as $3^{2} \cdot 3$ .

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Factor $9$ out of $27$ .

$c = \pm i \cdot \sqrt{9 (3)}$

Rewrite $9$ as $3^{2}$ .

$c = \pm i \cdot \sqrt{3^{2} \cdot 3}$

Pull terms out from under the radical.

$c = \pm i \cdot (3 \sqrt{3})$

Move $3$ to the left of $i$ .

$c = \pm 3 i \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the $\pm$ to find the first solution.

$c = 3 i \sqrt{3}$

Next, use the negative value of the $\pm$ to find the second solution.

$c = - 3 i \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

$c = 3 i \sqrt{3}, - 3 i \sqrt{3}$

Solve for c 2c^2+54=0

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